# seating arrangement

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• Aug 12th 2006, 08:20 AM
galactus
I am convinced both solutions are viable depending on what is asked for.

I posed this problem on another site for fun and this is the response I received:

**"Say, first of all, that the seats are numbered 1,...,8 and any two
arrangements in which at least one person has a different seat assignment
are different arrangements. The first girl has 8 choices of seat. The
second girl has 5 choices, but these are of two different kinds: if she
sits one seat away from the first (2 chairs), the third girl has three
choices, but if she sits two seats away (2 chairs) or 3 seats away (one
chair), the third girl has 2 choices. Thus there is a total of 8*2*3 +
8*3*2 = 8*12=96 ways for the girls to sit. The boys may sit as they please
in the 5 remaining seats, 5!, so 96*120 = 11520 arrangements. If the table
is spinning so that you can't see the numbers but can see the people next
to each other, then there are 11520/8 = 1440 perceptibly different
arrangements. If additionally the girls are identical triplets and the boys
identical quintuplets, then there are fewer still arrangements".

I didn't intend on stirring such debate when I brought up the 11520 :)

**Coutesy of mathnerds.com
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